Q. The moments of inertia of two freely rotating bodies $A$ and $B$ are $I_{A}$ and $I_{B\ }$ respectively. $I_{A} > \ I_{B}$ and their angular momenta are equal. If $K_{A}$ and $K_{B}$ are their kinetic energies, then
A) $K_{A} = \ K_{B}$
B) $K_{A}\ \neq K_{B}$
C) $K_{A} < \ K_{B}$
D) $K_{A} = \ 2K_{B}$
Explanation
(c) Kinetic energy $E = \frac{L^{2}}{2I}$
If angular momenta are equal, then $E \propto \frac{1}{I}$
Kinetic energy $E = K$ (given in problem)
If $I_{A} > I_{B}$ then $K_{A} < K_{B}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.